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A164003 Decimal expansion of exp(-Pi^2/2). 0
0, 0, 7, 1, 9, 1, 8, 8, 3, 3, 5, 5, 8, 2, 6, 3, 6, 5, 6, 0, 7, 8, 0, 1, 3, 6, 6, 3, 9, 6, 3, 7, 1, 2, 0, 2, 9, 5, 5, 3, 6, 2, 3, 1, 8, 0, 8, 1, 5, 9, 7, 9, 4, 7, 5, 5, 8, 0, 3, 7, 1, 8, 1, 2, 4, 1, 2, 1, 3, 1, 8, 8, 6, 9, 7, 5, 6, 6, 5, 0, 8, 9, 5, 9, 6, 1, 0, 7, 9, 4, 3, 9, 8, 6, 5, 6, 6, 2, 3, 3, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Arises in connection with the expansion (e i)^(Pi i) = e^(Pi i) * i^(Pi i) = -1 * exp(Pi i log i) = -exp(Pi i * Pi/2 i) = -exp(-Pi^2/2) = -0.00719188335582636560780136639...

One has to be careful about branches of multivalued complex functions. By definition (e i)^(Pi i) is exp(Pi i log(e i)) [using any of the branches of log] = exp(Pi i (1 + Pi i/2 + 2 n Pi i)) [ for any integer n ] = - exp(- Pi^2/2 - 2 n Pi^2). There is no imaginary part in any of its branches. If n=0 we get (-1) times the present constant.

LINKS

Table of n, a(n) for n=0..100.

EXAMPLE

.0071918833558263656078013663963712029553623180815979475580371...

MATHEMATICA

Join[{0, 0}, RealDigits[Exp[-Pi^2/2], 10, 120][[1]]] (* Harvey P. Dale, Jul 11 2011 *)

PROG

(PARI) exp(-Pi^2/2) \\ Charles R Greathouse IV, Mar 25 2014

CROSSREFS

Sequence in context: A019661 A200130 A284151 * A280704 A069609 A019855

Adjacent sequences:  A164000 A164001 A164002 * A164004 A164005 A164006

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane, Aug 06 2010, based on postings to the Sequence Fans Mailing List by Alonso Del Arte, Charles R Greathouse IV, Sean A. Irvine, Robert Israel and other correspondents.

STATUS

approved

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Last modified June 25 20:26 EDT 2017. Contains 288730 sequences.